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A statistical Markov chain approximation of transient hospital inpatient inventory

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  • Broyles, James R.
  • Cochran, Jeffery K.
  • Montgomery, Douglas C.

Abstract

Inventory levels are critical to the operations, management, and capacity decisions of inventory systems but can be difficult to model in heterogeneous, non-stationary throughput systems. The inpatient hospital is a complicated throughput system and, like most inventory systems, hospitals dynamically make managerial decisions based on short term subjective demand predictions. Specifically, short term hospital staffing, resource capacity, and finance decisions are made according to hospital inpatient inventory predictions. Inpatient inventory systems have non-stationary patient arrival and service processes. Previously developed models present poor inventory predictions due to model subjectivity, high model complexity, solely expected value predictions, and assumed stationary arrival and service processes. Also, no models present statistical testing for model significance and quality-of-fit. This paper presents a Markov chain probability model that uses maximum likelihood regression to predict the expectations and discrete distributions of transient inpatient inventories. The approach has a foundation in throughput theory, has low model complexity, and provides statistical significance and quality-of-fit tests unique to this Markov chain. The Markov chain is shown to have superior predictability over Seasonal ARIMA models.

Suggested Citation

  • Broyles, James R. & Cochran, Jeffery K. & Montgomery, Douglas C., 2010. "A statistical Markov chain approximation of transient hospital inpatient inventory," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1645-1657, December.
  • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1645-1657
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    2. Petropoulos, Fotios & Makridakis, Spyros & Assimakopoulos, Vassilios & Nikolopoulos, Konstantinos, 2014. "‘Horses for Courses’ in demand forecasting," European Journal of Operational Research, Elsevier, vol. 237(1), pages 152-163.
    3. Bekker, René & uit het Broek, Michiel & Koole, Ger, 2023. "Modeling COVID-19 hospital admissions and occupancy in the Netherlands," European Journal of Operational Research, Elsevier, vol. 304(1), pages 207-218.
    4. Kortbeek, N. & Braaksma, A. & Burger, C.A.J. & Bakker, P.J.M. & Boucherie, R.J., 2015. "Flexible nurse staffing based on hourly bed census predictions," International Journal of Production Economics, Elsevier, vol. 161(C), pages 167-180.

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